Thursday, April 14, 2022 - 12:30 in ZOOM - Video Conference
On the Ergodicity of Interacting Particle Systems under Number Rigidity
A talk in the Bielefeld Stochastic Afternoon series by
Kohei Suzuki
| Abstract: |
In this talk, under the assumption of the number rigidity of a
point process $\mu$ in the sense of Ghosh-Peres (Duke Math. J. '17), the
equivalence of the following three concepts is discussed: (a) the
ergodicity of infinitely many interacting particle diffusions with
invariant measure $\mu$; (b) the finiteness of 2-Wasserstein distance
between sets of $\mu$-positive measures; (c) the tail-triviality of
$\mu$.
As an application, the convergence to the equilibrium of interacting
particle diffusions is obtained in the case that $\mu$ is sine$_2$,
Airy$_2$, Bessel, and Ginibre point processes. In particular, our result
covers (unlabelled) Dyson Brownian motion. In the process of the proof,
we confirm the Sobolev-to-Lipschitz property, which was originally
conjectured by Röckner-Schied (J. Funct. Anal. '99).
Within the CRC this talk is associated to the project(s): A5, B1 |
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